Question

A 50-gallon tank initially contains 10 gallons of fresh water. At t = 0, a brine solution containing 2 pounds of salt per gallon is poured into the tank at a rate of 5 gal/min. The well-stirred mixture drains from the tank at a rate of 3 gal/min. Find the amount of salt in the tank at the moment of overflow. Please use differential equations to solve this problem and please put the answer in decimal form. I did this problem and got 124.8 pounds of salt as my answer and want to check if this is right.

Answer #1

A tank initially holds 100 gal of brine solution. At t = 0,
fresh water is poured into the tank at the rate of 5 gal/min, while
the well-stirred mixture leaves the tank at the same rate. After 20
min, the tank contains 20/e lb of salt. Find the initial
concentration of the brine solution inside the tank. Ans.: 0.20
lb/gal

A 110 gallon tank initially contains 5 lbs salt dissolved in 60
gallons of water. Brine containing 1 lb salt per gallon begins to
flow into the tank at the rate of 3 gal/min and the well-mixed
solution is drawn off at the rate of 1 gal/min. How much salt is in
the tank when it is about to overflow? (Round your answer to the
nearest integer.)

Using differential equation:
A 200- gallon tank initially contains 40 gallons of brine in
which 10 pounds of salt have been dissolved. Starting at t=0 ,
brine containing 5 pounds of salt per gallon flows into the tank at
rate of 6 gallons per minutes. At the same time, the well-stirred
mixture flows out of the tank at the slower rate of 4 gallons per
minute.
a)How much salt is in the tank at the end of t minutes?
b)...

A tank contains 30 gallons of brine solution containing 10 lb of
salt. Another brine solution of concentration of 3 lb/gallon is
poured into the tank at the rate of 2 gallons/min. The well stirred
solution in the tank is drained out at the rate of 2 gallons/min.
Let the amount of salt in the tank at time ? be ?(?).
Write the differential equation for A(t) and solve it.

suppose a large tank has 300 gallon of brine solution. Brine
sol. was being pumped into the tank at a rate of 3 gal/min. it
mixed with the solution there and then the mixture was pumped out
at the rate of 2 gal/min. the concentraion of salt in the inflo or
solution entering was 2 lb/gal. initially, 50 pounds of salt were
dissolved in the 300 gallons. Please answer clearly. Thank u.
a find the amount of salt in tank...

suppose a large tank has 300 gallon of brine solution. Brine
sol. was being pumped into the tank at a rate of 3 gal/min. it
mixed with the solution there and then the mixture was pumped out
at the rate of 2 gal/min. the concentraion of salt in the inflo or
solution entering was 2 lb/gal. initially, 50 pounds of salt were
dissolved in the 300 gallons.
find the amount of salt in tank at time t.
if the tank...

A 500-gallon tank initially contains 100gal of brine containing
50lb of salt. Brine containing 2lb of salt per gallon enters the
tank at the rate of 4gal per minute and the well stirred solution
leaves the tank at a rate of 8gal per minute.
(a) How long will it be before the tank is empty
(b) Determine the differential equation that gives the amount
A(t) of salt (in pounds) in the tank at any time t before it is
emptied....

A tank originally contains 100 gal of fresh water. Then water
containing
1
2
lb of salt per gallon is poured into the tank at a rate of 2
gal/min, and the mixture is allowed to leave at the same rate.
After 10 min the process is stopped, and fresh water is poured into
the tank at a rate of 3 gal/min,with the mixture again leaving at
the same rate. Find the amount of salt in the tank at the...

A tank contain 200 gallons of water. Five gallons of brine per
minute flow into the tank, each gallon of brine containing 1 pound
of salt. Five gallons of water flow out of the tank per minute.
Assume that the tank is kept well stirred. Find a differential
equation for the number of pounds of salt in the tank (call it y)
Assuming the tank intially contains no salt, solve this
differential equation. At what time will there be 100...

A tank originally contains 100 gal of fresh water. Then water
containing 1/2 lb of salt per gallon is poured into the tank at a
rate of 2 gal/min, and the mixture is allowed to leave at the same
rate. After 10 min the process is stopped, and fresh water is
poured into the tank at a rate of 5 gal/min, with the mixture again
leaving at the same rate. Find the amount of salt in the tank at
the...

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